$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}+2;}{\phantom{;}5x\phantom{;}+22\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2x\phantom{;}+2\overline{\smash{)}\phantom{;}5x^{3}+12x^{2}+14x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+2;}\underline{-5x^{3}+10x^{2}-10x\phantom{;}\phantom{-;x^n}}\\\phantom{-5x^{3}+10x^{2}-10x\phantom{;};}\phantom{;}22x^{2}+4x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+2-;x^n;}\underline{-22x^{2}+44x\phantom{;}-44\phantom{;}\phantom{;}}\\\phantom{;-22x^{2}+44x\phantom{;}-44\phantom{;}\phantom{;}-;x^n;}\phantom{;}48x\phantom{;}-40\phantom{;}\phantom{;}\\\end{array}$

$5x+22+\frac{48x-40}{x^2-2x+2}$